Sufficient LMI conditions for the design of static and reduced order controllers

In this paper we address the problem of designing static and reduced order dynamic controllers for linear continuous-time invariant systems. A new LMI controller parametrization is proposed allowing for the design of stable and strictly proper controllers. In the static output feedback case the Lyapunov function matrices do not appear in the controller parametrization. The results are illustrated through several examples.

[1]  Didier Henrion,et al.  Convergent relaxations of polynomial matrix inequalities and static output feedback , 2006, IEEE Transactions on Automatic Control.

[2]  A. Trofino,et al.  Robust, stable and reduced order dynamic output feedback controllers with guaranteed H/sub 2/ performance , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  J. Geromel,et al.  An LMI optimization approach to multiobjective controller design for discrete-time systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  Maciejowsk.  Multivariable Feedback Design , 1989 .

[5]  Pierre Apkarian,et al.  Nonsmooth optimization algorithm for mixed H2/H∞ synthesis , 2007, 2007 46th IEEE Conference on Decision and Control.

[6]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[7]  Y. Chou,et al.  Stable controller design for MIMO systems : an LMI approach , 2007 .

[8]  C. Scherer.  Mixed H2/H∞ control for time‐varying and linear parametrically‐varying systems , 1996 .

[9]  Guang-Hong Yang,et al.  Static Output Feedback Control Synthesis for Linear Systems With Time-Invariant Parametric Uncertainties , 2007, IEEE Transactions on Automatic Control.

[10]  B. De Schutter,et al.  A BMI optimization approach to robust output-feedback control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Y. Ebihara,et al.  New dilated LMI characterizations for continuous-time control design and robust multiobjective control , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[12]  Hitay Özbay,et al.  On the strong stabilization and stable Hinfinity-controller design problems for MIMO systems , 2000, Autom..

[13]  Adrian S. Lewis,et al.  Stabilization via Nonsmooth, Nonconvex Optimization , 2006, IEEE Transactions on Automatic Control.

[14]  Qing-Guo Wang,et al.  An Improved ILMI Method for Static Output Feedback Control With Application to Multivariable PID Control , 2006, IEEE Transactions on Automatic Control.

[15]  Daniel U. Campos-Delgado,et al.  A parametric optimization approach to H∞ and H2 strong stabilization , 2003, Autom..

[16]  Z. Luo,et al.  Computational complexity of a problem arising in fixed order output feedback design , 1997 .

[17]  Minyue Fu,et al.  Pole placement via static output feedback is NP-hard , 2004, IEEE Transactions on Automatic Control.

[18]  J. Löfberg.  Modeling and solving uncertain optimization problems in YALMIP , 2008 .

[19]  L. Jetto.  Strong stabilization over polytopes , 1999, IEEE Trans. Autom. Control..

[20]  José Claudio Geromel,et al.  H2-norm optimization with constrained dynamic output feedback controllers: decentralized and reliable control , 1999, IEEE Trans. Autom. Control..

[21]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[22]  Didier Henrion.  Solving static output feedback problems by direct search optimization , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[23]  H. Ito,et al.  Design of stable controllers attaining low Hinfinity weighted sensitivity , 1993, IEEE Trans. Autom. Control..

[24]  P. Dorato,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.